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Some results for the black-body radiation obtained in the context of the nonextensive statistical mechanics (normalized approach) are analyzed. Since the obtained elsewhere thermodynamic potential can be expressed in terms of Wright's special function a useful asymptotic expansion can be obtained. This expansion allows to consider in a simple way the thermodynamic properties of the black-body radiation away from the Boltzmann–Gibbs limit q→1. The proposed approximation scheme is physically reasonable for the analysis of the cosmic background radiation. It is shown that while the internal energy remains extensive the application of the concepts of the nonextensive lead to the Td+1 Stefan–Boltzmann behavior.  相似文献
2.
We have constructed an embedded-atom potential for Fe by fitting to both experimental and first-principles results. The potential reproduces with satisfactory accuracy the lattice properties, surface energies and point defect energies for both BCC and the high temperature FCC phases of the metal. The potential was used in tandem with molecular-dynamics simulations to calculate the thermal expansion of both BCC-Fe and FCC-Fe, the phonon dispersion curves, mean-square displacements and surface relaxations of the element. In addition, we have studied self-diffusion of single adatoms on the BCC-Fe(1 0 0) surface at several temperatures. The migration energies and pre-exponential factors for three main diffusion mechanisms were determined and compared with available experimental data. We have found that the diagonal exchange diffusion process is energetically favored over the direct hopping mechanism and that its migration energy is close to the experimental value. Furthermore, the diffusion coefficient associated with the diagonal exchange diffusion process is about an order of magnitude higher than those of the hopping and the non-diagonal exchange mechanisms.  相似文献
3.
The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r - (d + σ), where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001  相似文献
4.
Generalized xy lattice spin models consist of three-component unit vectors, associated with a D-dimensional lattice (say ), parameterized by usual spherical angles (θkk), and interacting via a ferromagnetic potential restricted to nearest neighbours, of the form here epsilon is a positive quantity setting energy and temperature scales. The models were recently introduced, and proven to support an ordering transition taking place at finite temperature when D=3; in turn, this transition had been investigated by different techniques for p=2,3,4, and found to belong to the same universality class as the xy model (i.e. p=1). More recently, it was rigorously proven that for sufficiently large p the transition becomes first order. Here we present a detailed analysis of the transitional properties of this class of models for selected values of p. For p=8 simulation results showed a second order phase transition belonging to the xy class of universality; they suggested tricritical behaviour for p=12, and gave evidence of first-order transitions for both p=16 and p=20.  相似文献
5.
In this paper we study a recent generalization of the XY-model in two dimensions by using Monte Carlo method. The vortex density, specific heat, energy and critical temperature are obtained. Some results are compared with approximated analytical calculations. The nature of the phase transition as the generalization parameter varies is discussed.  相似文献
6.
The finite-size critical properties of the (n) vector ϕ4 model, with long-range interaction decaying algebraically with the interparticle distance r like r -d - σ, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d < = σ) and the upper ( d > = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001  相似文献
7.
A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999  相似文献
8.
The finite-size shift of the critical temperature is calculated by the example of the spherical model, with short- and long-range interactions, confined to the general geometryL d–d × d subject to periodic boundary conditions. The derived formula unifies in some sense all results found up to now.  相似文献
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